Find the Tangent Given the Point (25/313,312/313)

$(\frac{25}{313}, \frac{312}{313})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{25}{313}, \frac{312}{313})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{25}{313}, 0)$ , and $(\frac{25}{313}, \frac{312}{313})$ .

Opposite : $\frac{312}{313}$

Adjacent : $\frac{25}{313}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{312}{313}}{\frac{25}{313}}$ .

$\frac{\frac{312}{313}}{\frac{25}{313}}$

Step 3

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{312}{313} \cdot \frac{313}{25}$

Cancel the common factor of $313$ .

Cancel the common factor.

$\tan (θ) = \frac{312}{313} \cdot \frac{313}{25}$

Rewrite the expression.

$\tan (θ) = 312 (\frac{1}{25})$

Combine $312$ and $\frac{1}{25}$ .

$\tan (θ) = \frac{312}{25}$

Step 4

Approximate the result.

$\tan (θ) = \frac{312}{25} \approx 12.48$

Find the Tangent Given the Point (25/313,312/313)

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